The Logical Structure of Algorithms

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• published: 02 Jun 2016
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Don't hesitate to comment below if you have any questions or additional phrases The Logical Structure of Algorithms ,Algorithms Steps necessary to complete a task or solve a problem. Example: Recipe for baking a cake Will contain a list of ingredients Step-by-step instructions on what to do with those ingredients A recipe provides an algorithm for baking a cake. ,Other algorithms When you learned the process for doing long division you learned an algorithm. The Holtrop and Mennen Algorithm, used by naval architects to design the optimum propellers for a ship, contains thousands of steps. ,Algorithms are sequential Usually we can think of the instructions in an algorithm as being executed one at a time. They form what is sometimes called a sequential logic. This is only part of the story, however… As a software developer you need to be able to design, manipulate, and implement sequential algorithms ,Common patterns There are a small set of patterns that exist in the design of sequential logic. These patterns fall into categories that form the elements of logical structure. They can be combined in myriad ways to form the logical structure of algorithms. A software developer familiar with the design patterns of logical structure can more easily create and modify software. ,Plumbers ,Plumbers In the design of the plumbing for a new building, architects have a selection of parts from which to build the system. T-joints Elbow joints Many kinds of valves Etc. Architects need to know how the individual parts work. And how they fit together. ,Elements of logical structure There are only a handful of basic elements that a software developer need learn. In the 1960s Bohm and Jacopinini showed that algorithms are composed of three major structures: Linear sequences Branching routines Loops Modern computer programming focuses on these three elements of logical structure. ,Flowcharts ,Flowcharts Bohm and Jacopini were not the first to use flowcharts but they were the first to formalize the process. They used a simple system, two symbols Rectangles to show each step in an algorithm Diamond-shaped boxes to show a decision step or condititional. We will use one additional symbol, an oval, to mark the beginning and end of an algorithm. ,Flowchart symbols ,Terminators There should be only one terminator at the beginning of an algorithm and one at the end. Each algorithm should have one entry point (beginning) and one exit point (end). ,Linear sequences The simplest element of logical structure is a linear sequence. One instruction follows another in a straight line. No branching No looping ,Linear sequence ,Linear Sequences Deceptively simple Must meet the following criteria: Entry and exit conditions need to be clear: What conditions need to exist before the sequence starts? What can we expect the situation to be when the sequence is finished? Must be complete; don’t leave out necessary steps. Steps must be in proper order Each individual instruction must be correct; if one step is wrong, the entire algorithm is wrong. Example: driving directions” What if you leave out a turn? What if you say to turn left, when you should have said right? ,In short Linear sequences must… Have clearly stated entry and exit conditions Be complete Be organized in the proper order ,Selection Sequences Sometimes an algorithm reaches a point where the sequence of steps can go one direction or another (a fork in the road). This is called a selection sequence. Also called a conditional or branching routine ,Selection Sequences Consider a student who has a chemistry lab at 2pm on Fridays only: Start If (Today is Friday) Then (Get to lab by 2pm) ,Selection Sequence Example ,In Summary Selection sequence occurs whenever the path of sequential logic (steps) in an algorithm splits into two or more paths. Each path is called a branch. ,Binary and Multiple Branching If there are two possible paths, then the routine is known as binary branching. If there are more than two paths, multiple branching. Binary branching: “Woul

The Logical Structure of Algorithms

• Report rights infringement
• published: 02 Jun 2016
• views: 81

Don't hesitate to comment below if you have any questions or additional phrases The Logical Structure of Algorithms ,Algorithms Steps necessary to complete a task or solve a problem. Example: Recipe for baking a cake Will contain a list of ingredients Step-by-step instructions on what to do with those ingredients A recipe provides an algorithm for baking a cake. ,Other algorithms When you learned the process for doing long division you learned an algorithm. The Holtrop and Mennen Algorithm, used by naval architects to design the optimum propellers for a ship, contains thousands of steps. ,Algorithms are sequential Usually we can think of the instructions in an algorithm as being executed one at a time. They form what is sometimes called a sequential logic. This is only part of the story, however… As a software developer you need to be able to design, manipulate, and implement sequential algorithms ,Common patterns There are a small set of patterns that exist in the design of sequential logic. These patterns fall into categories that form the elements of logical structure. They can be combined in myriad ways to form the logical structure of algorithms. A software developer familiar with the design patterns of logical structure can more easily create and modify software. ,Plumbers ,Plumbers In the design of the plumbing for a new building, architects have a selection of parts from which to build the system. T-joints Elbow joints Many kinds of valves Etc. Architects need to know how the individual parts work. And how they fit together. ,Elements of logical structure There are only a handful of basic elements that a software developer need learn. In the 1960s Bohm and Jacopinini showed that algorithms are composed of three major structures: Linear sequences Branching routines Loops Modern computer programming focuses on these three elements of logical structure. ,Flowcharts ,Flowcharts Bohm and Jacopini were not the first to use flowcharts but they were the first to formalize the process. They used a simple system, two symbols Rectangles to show each step in an algorithm Diamond-shaped boxes to show a decision step or condititional. We will use one additional symbol, an oval, to mark the beginning and end of an algorithm. ,Flowchart symbols ,Terminators There should be only one terminator at the beginning of an algorithm and one at the end. Each algorithm should have one entry point (beginning) and one exit point (end). ,Linear sequences The simplest element of logical structure is a linear sequence. One instruction follows another in a straight line. No branching No looping ,Linear sequence ,Linear Sequences Deceptively simple Must meet the following criteria: Entry and exit conditions need to be clear: What conditions need to exist before the sequence starts? What can we expect the situation to be when the sequence is finished? Must be complete; don’t leave out necessary steps. Steps must be in proper order Each individual instruction must be correct; if one step is wrong, the entire algorithm is wrong. Example: driving directions” What if you leave out a turn? What if you say to turn left, when you should have said right? ,In short Linear sequences must… Have clearly stated entry and exit conditions Be complete Be organized in the proper order ,Selection Sequences Sometimes an algorithm reaches a point where the sequence of steps can go one direction or another (a fork in the road). This is called a selection sequence. Also called a conditional or branching routine ,Selection Sequences Consider a student who has a chemistry lab at 2pm on Fridays only: Start If (Today is Friday) Then (Get to lab by 2pm) ,Selection Sequence Example ,In Summary Selection sequence occurs whenever the path of sequential logic (steps) in an algorithm splits into two or more paths. Each path is called a branch. ,Binary and Multiple Branching If there are two possible paths, then the routine is known as binary branching. If there are more than two paths, multiple branching. Binary branching: “Woul